First and only edition, including the two rare supplements, of a work on quadrature that the author calls a "new very simple theory for squaring curved surfaces based on the summation of infinite series," intended to make differential and integral calculus unnecessary. His goal is to demonstrate the usefulness of sums of infinite series in place of differential and integral calculus. The 1811 review found little new in Fresenius's "theory" and noted its similarity to the methods of John Wallis's 1656 Arithmeticam Infinitorum. Little is known about the author, who signed only the dedications, but parts 1 and 2 are dedicated to teachers, suggesting he was still young. Fresenius is therefore probably the identically named author of a half dozen works on religion, history and education published in Frankfurt in the years 1836 to 1853, including Zur Geschichte der Erfindung des Buchdrucks.
In very good condition, with part 3 slightly browned and its edges tattered. An immature mathematical work by a curious author, with the rare supplements containing clues to his early life. Jenaische Allg. Literatur-Zeit. VIII.II (no. 110, 15 May 1811); KVK (5, 3 & 1 copies); WorldCat (4, 1 & 1 copies).